COVARIANCE ANALYSIS OF TIME-DELAY ESTIMATES FOR STRAINED SIGNALS

Estimates of time-varying delays from the ultrasonic echo signals of c ompressed biological media are the basis of a new type of medical imag ing known as elastography. This paper is focused on predicting the cov ariance between time delays estimated from sequential, Gaussian;weight ed echo segments that overlap. The accuracy of the analysis was tested and improved by comparisons with measurements involving ultrasonic wa veforms simulated from independent band-limited Gaussian signal and no ise spectra, Data were generated to explore the dependence of time del ay covariance on ultrasonic signal-to-noise ratio, time-bandwidth prod uct W, fractional bandwidth, window separation, and the amount of stra in (a is the time rate of change in delay). The relationship between a and other experimental parameters was crucial for understanding how s ignal decorrelation affects time delay error and, ultimately, elastogr aphic noise, For echo waveforms without strain (a = 0), delay variance was found to decrease with W. However, when waveform segments were st rained (a not equal 0) a minimum was found in the plot of time delay v ariance versus W, where delay errors from additive noise equaled those from signal decorrelation caused by, strain. Der lay covariance decre ased monotonically with increasing window separation (less overlap) wh en a = 0, When a not equal 0, however, the covariance became negative for large separations. Properties of strain image noise were predicted from knowledge of the experimental parameters and time delay errors.